Environmental time series analysis and forecasting with the Captain toolbox

The Data-Based Mechanistic (DBM) modelling philosophy emphasises the importance of parametrically efficient, low order, 'dominant mode' models, as well as the development of stochastic methods and the associated statistical analysis required for their identification and estimation. Furthermore, it stresses the importance of explicitly acknowledging the basic uncertainty in the process, which is particularly important for the characterisation and forecasting of environmental and other poorly defined systems. The paper focuses on a Matlab^(R) compatible toolbox that has evolved from this DBM modelling research. Based around a state space and transfer function estimation framework, Captain extends Matlab^(R) to allow, in the most general case, for the identification and estimation of a wide range of unobserved components models. Uniquely, however, Captain focuses on models with both time variable and state dependent parameters and has recently been implemented with the latest methodological developments in this regard. Here, the main innovations are: the automatic optimisation of the hyper-parameters, which define the statistical properties of the time variable parameters; the provision of smoothed as well as filtered parameter estimates; the robust and statistically efficient identification and estimation of both discrete and continuous time transfer function models; and the availability of various special model structures that have wide application potential in the environmental sciences.

[1]  Peter C. Young,et al.  Recursive Estimation and Time Series Analysis , 1984 .

[2]  Markos Papageorgiou.  Traffic and Transportation Systems , 1992, Concise Encyclopedia of Modelling & Simulation.

[3]  Rik Pintelon,et al.  An Introduction to Identification , 2001 .

[4]  Walerian Kipiniak,et al.  Optimal Estimation, Identification, and Control , 1964 .

[5]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[6]  P. Young,et al.  Stochastic, Dynamic Modelling and Signal Processing: Time Variable and State Dependent Parameter Estimation , 2000 .

[7]  P. Young,et al.  Refined instrumental variable methods of recursive time-series analysis Part III. Extensions , 1980 .

[8]  Peter C. Young,et al.  Identification of a multivariable state dependency for airflow rate in a forced ventilation test chamber. , 2004 .

[9]  Diego J. Pedregal,et al.  Recursive Fixed Interval Smoothing and the Evaluation Of Lidar Measurements: A Comment On The Paper By Holst, Hössjer, Björklund, Ragnarsson And Edner. , 1996 .

[10]  Allan E Pearson.  Control of Non-Linear Systems. , 1976 .

[11]  Peter C. Young,et al.  Recursive estimation and forecasting of non‐stationary time series , 1990 .

[12]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[13]  J. P. Norton.  Identification by optimal smoothing using integrated random walks , 1976 .

[14]  P. Young.  AN INSTRUMENTAL VARIABLE APPROACH TO ARMA MODEL IDENTIFICATION AND ESTIMATION , 2006 .

[15]  Peter C. Young,et al.  Proportional-integral-plus (PIP) control of non-linear systems. , 2000 .

[16]  Peter C. Young,et al.  System identification, time series analysis and forecasting : The Captain Toolbox handbook. , 2007 .

[17]  Eric R. Ziegel,et al.  Developments in Time Series Analysis , 1993 .

[18]  Peter C. Young,et al.  Data-Based Mechanistic Modeling of Engineering Systems , 1998 .

[19]  P. C. Young,et al.  System Identification , Time Series Analysis and Forecasting , 2007 .

[20]  David Henry,et al.  Development of an operational model-based warning system for tropospheric ozone concentrations in Bordeaux, France , 2004, Environ. Model. Softw..

[21]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[22]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[23]  M. G. Anderson.  Encyclopedia of hydrological sciences. , 2005 .

[24]  Nathan S. Balke.  Detecting Level Shifts in Time Series , 1993 .

[25]  Peter C. Young,et al.  The Validity and Credibility of Models for Badly Defined Systems , 1983 .

[26]  Peter C. Young,et al.  Data-based mechanistic modelling of environmental, ecological, economic and engineering systems. , 1998 .

[27]  Daniel Berckmans,et al.  Data-Based Mechanistic Modelling (DBM) and control of mass and energy transfer in agricultural buildings , 1999 .

[28]  M. B. Beck,et al.  Uncertainty and forecasting of water quality , 1983 .

[29]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[30]  Peter C Young,et al.  Advances in real–time flood forecasting , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  G. Cobb.  The problem of the Nile: Conditional solution to a changepoint problem , 1978 .

[32]  C. James Taylor,et al.  Environmental Test Chamber for the Support of Learning and Teaching in Intelligent Control , 2004 .

[33]  P. Young,et al.  Simplicity out of complexity in environmental modelling: Occam's razor revisited. , 1996 .

[34]  Fred C. Schweppe,et al.  Evaluation of likelihood functions for Gaussian signals , 1965, IEEE Trans. Inf. Theory.

[35]  H. Akaike.  A new look at the statistical model identification , 1974 .

[36]  Peter C. Young,et al.  The Identification and Estimation of Nonlinear Stochastic Systems , 2001 .

[37]  Michael A. West,et al.  Bayesian forecasting and dynamic models (2nd ed.) , 1997 .

[38]  P. Young.  Optimal IV identification and estimation of continuous-time TF models , 2002 .

[39]  Peter C. Young,et al.  Nonlinear and Nonstationary Signal Processing , 1998, Technometrics.

[40]  Peter C. Young,et al.  The Instrumental Variable Method: A Practical Approach to Identification and System Parameter Estimation , 1985 .

[41]  P. Young,et al.  Refined instrumental variable methods of recursive time-series analysis Part I. Single input, single output systems , 1979 .

[42]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[43]  Daniel Berckmans,et al.  Cost effective combined axial fan and throttling valve control of ventilation rate , 2004 .

[44]  María Dolores Ruiz-Medina,et al.  A study on sensitivity of spatial sampling designs to a priori discretization schemes , 2005, Environ. Model. Softw..

[45]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[46]  Ali Zolghadri,et al.  Adaptive nonlinear state-space modelling for the prediction of daily mean PM10 concentrations , 2006, Environ. Model. Softw..

[47]  P. Young,et al.  Time variable and state dependent modelling of non-stationary and nonlinear time series , 1993 .

[48]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[49]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[50]  A. Heber,et al.  Air Patterns and Turbulence in an Experimental Livestock Building , 1996 .

[51]  Peter C. Young,et al.  Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis , 1999 .

[52]  Peter C. Young,et al.  Identification and system parameter estimation , 1985 .

[53]  J. Norton.  Optimal smoothing in the identification of linear time-varying systems , 1975 .

[54]  P. Young,et al.  Dynamic harmonic regression. , 1999 .

[55]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[56]  David Q. Mayne,et al.  Optimal Non-stationary Estimation of the Parameters of a Linear System with Gaussian Inputs † , 1963 .

[57]  Peter C. Young,et al.  Macroscopic traffic flow modelling and ramp metering control using Matlab/Simulink , 2004, Environ. Model. Softw..

[58]  Kumpati S. Narendra,et al.  Identification and control , 1998 .